CAPE CANAVERAL, Fla. — NASA’s newest delivery service made its first-ever shipment to the International Space Station on Sunday, another triumph for a booming commercial space arena that has its sights set on launching astronauts.

Orbital Sciences Corp.’s unmanned cargo ship, Cygnus, pulled up at the orbiting lab with a half-ton of meals and special treats for the station astronauts who assisted in the high-flying feat.

With the smooth linkup, Orbital Sciences, of Virginia, became only the second company to accomplish such a far-flung shipment. The California-based SpaceX company took the lead last year.

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National Aeronautics and Space Administration officials along with White House representatives declared it a historic day. ‘‘It was just a very, very impressive job . . . I just couldn’t be happier and more proud,’’ said the NASA manager overseeing this commercial effort, Alan Lindenmoyer.

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Now that the space station has two US private companies capable of delivering goods, he noted, ‘‘it’s certainly a relief and something we’re ready to celebrate.’’

All this was a week late in coming.

The Cygnus — named after the swan constellation — should have arrived a week earlier, four days after its launch from Virginia on Sept. 18. But a discrepancy in navigational data between the capsule and the space station led to a frustrating standoff. A simple software repair was carried out by ground controllers. Then the Cygnus had to wait for a Russian spacecraft to bring three new astronauts.

The wait involved ‘‘some hair-pulling and heartache,’’ said Orbital Sciences executive vice president Frank Culbertson. But in the end, the company’s patience was rewarded with a perfect rendezvous demonstration.

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Applause could be heard in Mission Control once Italian astronaut Luca Parmitano grabbed hold of Cygnus with the space station’s hulking mechanical arm. The union occurred 260 miles above the Indian Ocean. Before long, the capsule was latched securely to the orbiting lab. Its hatch was to remain closed until early Monday; that’s when the six station astronauts were to enter the capsule and begin unloading the bounty.

The successful arrival means Orbital Sciences can start making good on a $1.9 billion contract with NASA for more Cygnus deliveries, each one carrying more and more cargo.

The next one could fly by Christmas.

‘‘We have a big incentive ahead of us,’’ said Culbertson, a former astronaut who lived on the space station a decade ago.

John Holdren, assistant to President Obama for science and technology, said that Sunday’s success validates the president’s goal of focusing NASA on deep-space exploration and leaving station cargo and astronaut hauls to private industry.

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‘‘Space history was made again today,’’ Holdren said in a statement.

Sunday’s operation was the culmination of several years of effort for Orbital Sciences, which was hired by NASA along with SpaceX — formally Space Exploration Technologies Corp. — to keep the space station well stocked in this post-shuttle era.

‘‘To our great friend and colleague G. David Low. ... This one’s for you,’’ Orbital Sciences said via Twitter.